Principal parametric resonance analysis of a rotating agglomerated nanocomposite beam employing the Chebyshev–Ritz method

Abstract

The dynamic instability owing to a principal parametric resonance of a rotating agglomerated nanocomposite beam reinforced with randomly oriented carbon nanotubes (a CNTRC beam) in a uniform thermal ambient is explored. The rotation speed fluctuates as a simple harmonic function of time around a mean value. A method on the basis of the Mori–Tanaka’s approach is implemented to determine the effective thermo-elastic constants of the agglomerated CNTRC beam. By considering the excitation frequency of the rotating speed two times the one of longitudinal or flapping natural frequencies, the principal parametric resonance is activated. The Bolotin’s technique and the Floquet theory are implemented to illuminate the instability region of the rotating agglomerated CNTRC beam. The impacts of the agglomeration parameters, and the CNT volume fraction on dynamic stability boundaries are illustrated. The outcomes reveal that for a rotating completely (partially) agglomerated CNTRC beam, the enlargement of the ratio of the inclusions volume with respect to the volume of the nanocomposite (the decrease in the ratio of the volume of the CNT within the inclusions with respect to the total volume of CNTs), reduces the instability region of the first flapping mode. Meanwhile, the required excitation dynamic amplitude for the activation of the dynamic instability improves.